Suspension flow modeling for general geometries

The flow of concentrated suspensions is well known to be accompanied by irreversible bulk migrations. One approach to modeling the migration of particles relative to the bulk motion is based on a particle flux induced by spatial variation of the particle normal stresses. A frame-invariant formulation of the mixture stresses is presented in a general form and used in this approach; specific forms of the constitutive model for the stress are considered. These forms either include only the isotropic shear-induced particle stress (particle pressure) or include both normal stress differences and the particle pressure. The predicted flow and migration behavior are considered for complex geometries, using the flows in a contraction and an expansion as the primary examples. Results are limited to two-dimensional flows.